New equations for Nusselt number and friction factor of the annulus side of the conically coiled tubes in tube heat exchangers

[Display omitted] •The Nusselt number increases with increase of the dimensionless pitch.•The friction factor decreases with increase of the dt,o/dt,i.•The Nusselt number is proportion with with Re0.81 and Pr0.39.•Equations are proposed for the Nusselt number and the friction factor estimation. Three dimensional simulation of heat transfer (turbulent/laminar) and fluid flow of water through the annulus side of conically tube heat exchangers is presented in this study. This study shows an accurate and clear results which were not available before. Realizable K-ɛ model is chosen for perusing the turbulence influences. The influence of operational and geometrical characteristics on the Friction factor and the Nusselt number is obtained. The results show if the cone angle increases from 0° to 90° the Friction factor and the Nusselt number increase by 15.51% and 37.17%, respectively. Furthermore, it is concluded that if the dimensionless ratio of the outer tube diameter to the inner one increases by 50% the Nusselt number increases by 39.11% while the friction factor decreases by 23.29%. The outcomes of this study proposed two new correlations (that cannot be found in the previous studies) to estimate the friction factor and the Nusselt number of the annulus side of these heat exchangers. These proposed equations are necessary and important for engineering applications involving designs of these heat exchangers. Furthermore, the current results are validated using the experimental data available in the literature. This validation shows an average error of only 9.87% in calculating Nusselt numbers, which is more accurate than any other predictive equations available in the literature.